Near-Linear-Phase IIR Filters Using Gauss-Newton Optimization

In this paper, we present a simple optimization-based method for designing near-linear-phase IIR filters based on the Gauss-Newton method, and we explore its benefits over symmetric FIR filters. We demonstrate IIR low-pass filters with lower group delay, lower order, and lower magnitude errors than corresponding FIR filters while still maintaining a phase response linearity of R2 ≥ 0.99 in the passband. Such filters can be beneficial in applications where approximate, rather than exact, linear phase is sufficient. Code is available on the author’s website.